Not your keys - not your coins, that's 100% true but for some people, I would say: Even your keys - not your coins.
Okay, woud love to hear opinion about this from the community members.
As we know and from every logic, we shouldn't trust web wallets and also exchanges. There were a lot of accidents when exchanges were hacked and people lost their coins. Some may say - don't keep your coins at exchanges for a long time but I would say that everything happens in seconds, maybe you had access on your coins at exchanges while you were replying to this thread but once you submitted the post, exchange got hacked and coins were lost, everything happens in seconds, otherwise loss wouldn't occur.
So, how do you trade in these cases? Only p2p exchanges? But it's not flexible and you may miss a good time frames where you could profit 1-2% of your balance.
It's not that you shouldn't be using exchanges per se, it's just that you shouldn't leave your entire holdings on exchanges(which surprisingly a lot of people still do). If you trade with like 5% of your total holdings, then only leave that 5% on exchanges. And just withdraw the funds when you plan on stopping trading for a while and such.